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Factor completely: (x-8)^(5)+(x-8)^(6) Answer:

Factor completely:\newline(x−8)5+(x−8)6 (x-8)^{5}+(x-8)^{6} \newlineAnswer:

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Full solution

Q. Factor completely:\newline(x−8)5+(x−8)6 (x-8)^{5}+(x-8)^{6} \newlineAnswer:
  1. Identify Common Factor: Identify the common factor in both terms.\newlineBoth terms have a common factor of (x−8)5(x-8)^5.
  2. Factor Out Common Factor: Factor out the common factor from both terms.\newlineWe can factor out (x−8)5(x-8)^{5} from both terms to get (x−8)5×[1+(x−8)](x-8)^{5} \times [1 + (x-8)].
  3. Simplify Inside Brackets: Simplify the expression inside the brackets.\newlineSimplify the expression inside the brackets to get (x−8)5×(x−8+1)(x-8)^{5} \times (x-8+1).
  4. Combine Like Terms: Combine like terms inside the brackets.\newlineCombine −8-8 and +1+1 to get −7-7, so the expression becomes (x−8)5⋅(x−7)(x-8)^{5} \cdot (x-7).
  5. Write Final Form: Write the final factored form.\newlineThe completely factored form of the expression is (x−8)5×(x−7)(x-8)^{5} \times (x-7).

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